This invention relates to a uniform magnetic field coil and, more particularly, to a uniform magnetic field coil, for example, for magnetic resonance imaging, capable of increasing the tolerable error of dimensions in its fabrication condition and of readily compensating irregular magnetic field components based on the error in dimensions.
FIG. 1 shows a prior-art uniform magnetic field coil with a notch, which is disclosed, for example in the thesis entitled "High Homogenious Field Superconducting Magnet" written by Teruo Noguchi on pages 241-251 of Japanese Magazine "Low Temperature Engineering", vol. 11, No. 6 (1976). FIG. 1 is a sectional view in the longitudinal direction of a cylindrical coil 1 with a notch. By utilizing a notched construction, the spacial distribution of the magnetic field near a coordinate origin O becomes uniform. The coil 1 is symmetrical with respect to a plane passing through the coordinate origin O perpendicular to the Z-axis and denoted by the symbol R as shown in FIG. 1. The magnetic filed Hz produced at a point Q is given by the following equation (1): EQU Hz=ja.sub.1 {F+FE.sub.2 (.rho./a.sub.1).sup.2 P.sub.2 (u)+FE.sub.4 (.rho./a.sub.1).sup.4 P.sub.4 (u) EQU +FE.sub.6 (.rho./a.sub.1).sup.6 P.sub.6 (u)+FE.sub.8 (.rho./a.sub.1).sup.8 P.sub.8 (u)+ . . . } (1)
where j=current density in the coil, PA1 a.sub.1 =inner diameter of the coil, PA1 .rho.=distance between the origin and the point Q, PA1 u=cos .theta., PA1 .theta.=angle formed between the line segment OQ and the z-axis PA1 F, FE.sub.n =function of the sectional shape of the coil, PA1 P(u)=Legendre function.
The first term of the right-hand side of equation (1) is a spatially uniform component independent of position (.rho., .theta.), but all the terms other than the first term are dependent upon position, i.e., the irregular components in space. In the uniform magnetic field coil, the spacial distribution of the magnetic field is uniform in the range where (.rho./a.sub.1)&lt;1. As described above, since (.rho./a.sub.1)&lt;1, if terms are sequentially set to zero starting with the terms of lower degree of (.rho./a.sub.1), then higher uniformity of the magnetic field can be attained. In the prior-art coil shown in FIG. 1, the first term of the right-hand side of the equation (1) is set to a predetermined value, and the second and third terms are set to 0 by controlling the sectional shape of the coil. EQU ja.sub.1 F=H.sub.0 ( 2) EQU FE.sub.2 =0 (3) EQU FE.sub.4 =0 (4)
where H.sub.0 denotes the magnetic field which is necessary for the magnetic resonance imaging. Since the coil inner diameter a.sub.1, the coil length 2b and the current density j are ordinarily given coil design conditions, the parameters taken as design parameters are the two types of coil outer diameters a.sub.2, a.sub.N and the notch length 2b.sub.N, each parameter denoting its corresponding dimension, as shown in FIG. 1. Since there are three equations relating to the design parameters (i.e., equations (2), (3) and (4)), these designing parameters a.sub.2, a.sub.N and 2b.sub.N can be individually determined.
In a coil designed in this manner, an irregular magnetic field component is introduced by the presence of terms of degree 6 or higher in the right-hand side of equation (1). Therefore, the coil obtained by the above design is called "sextic compensation coil". If the sectional shape of the coil is made more complicated to increase the number of design parameters, then the number of irregular magnetic field components which can be set to zero increases, with the result that a uniform magnetic field coil capable of compensating in a higher degree can be designed. In fact, the lower degree term of the irregular magnetic field might be generated by the influence of dimensional error present in the manufacturing process of the coil and the presence of an iron body near the coil, although a coil based on a predetermined design concept such as that outlined above, for example, is still referred to as a "sextic compensation coil". Besides, the irregular magnetic field component actually generated is ordinarily removed by installing a special correcting coil called "shim coil" (not shown) for generating only the component of the irregular magnetic field on the outer periphery of the coil 1 in FIG. 1.
Since the prior-art uniform magnetic field coil is constructed as described above, the finishing accuracy of the sectional shape of the coil must be extremely good, and therefore, the prior-art coil has the drawback that manufacturing is very difficult. Further, said coil has another drawback that some special means such as a shim coil or the like must be employed in order to remove the irregular magnetic field generated due to dimensional error in the manufacturing process.